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A Quadrature-Based Kinetic Model for Dilute Non-Isothermal Granular Flows

Published online by Cambridge University Press:  20 August 2015

Alberto Passalacqua
Affiliation:
Department of Chemical and Biological Engineering, Iowa State University, Ames, IA 50011-2230, USA
Janine E. Galvin
Affiliation:
United States Department of Energy National Energy Technology Laboratory, Morgantown, WV 26507-0880, USA
Prakash Vedula
Affiliation:
School of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, OK 73019-0601, USA
Christine M. Hrenya
Affiliation:
Department of Chemical and Biological Engineering, University of Colorado, Boulder, CO 80309-0424, USA
Rodney O. Fox
Affiliation:
Department of Chemical and Biological Engineering, Iowa State University, Ames, IA 50011-2230, USA
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Abstract

A moment method with closures based on Gaussian quadrature formulas is proposed to solve the Boltzmann kinetic equation with a hard-sphere collision kernel for mono-dispersed particles. Different orders of accuracy in terms of the moments of the velocity distribution function are considered, accounting for moments up to seventh order. Quadrature-based closures for four different models for inelastic collision-the Bhatnagar-Gross-Krook, ES-BGK, the Maxwell model for hard-sphere collisions, and the full Boltzmann hard-sphere collision integral-are derived and compared. The approach is validated studying a dilute non-isothermal granular flow of inelastic particles between two stationary Maxwellian walls. Results obtained from the kinetic models are compared with the predictions of molecular dynamics (MD) simulations of a nearly equivalent system with finite-size particles. The influence of the number of quadrature nodes used to approximate the velocity distribution function on the accuracy of the predictions is assessed. Results for constitutive quantities such as the stress tensor and the heat flux are provided, and show the capability of the quadrature-based approach to predict them in agreement with the MD simulations under dilute conditions.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2011

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